A handful of provisions tucked into a pair of must-pass bills under consideration in Congress this month could reshape the financing of political campaigns and give further cover to donors who want to keep their contributions private.

One measure would roll back limits on churches, which are prohibited under current law from advocating for candidates because of their tax-exempt status.

Other changes would relax rules affecting secret and wealthy donors and increase the amount of cash that political parties could spend on candidates.

The adjustments are being considered in the form of “riders,” or provisions that are tacked on to unrelated bills. Such attachments are controversial because they can pass without a separate vote or debate. The maneuver also masks the identity of the member of Congress who proposed each change.

In this case, lawmakers have attached them to House and Senate versions of appropriations bills, which must pass this month to keep the government operational. Ultimately, one or more may be dropped as part of budget negotiations, but the proposals have nevertheless drawn a sharp rebuke from government watchdog groups.

On Thursday, a coalition of two dozen such groups released a letter urging Congress to reject these riders.